A15508. Two Permutations

You are given three integers $n$ , $a$ , and $b$ . Determine if there exist two permutations $p$ and $q$ of length $n$ , for which the following conditions hold:

- The length of the longest common prefix of $p$ and $q$ is $a$ .
- The length of the longest common suffix of $p$ and $q$ is $b$ .

A permutation of length $n$ is an array containing each integer from $1$ to $n$ exactly once. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ( $2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ( $n=3$ but there is $4$ in the array).

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1\leq t\leq 10^4$ ) — the number of test cases. The description of test cases follows.

The only line of each test case contains three integers $n$ , $a$ , and $b$ ( $1\leq a,b\leq n\leq 100$ ).

For each test case, if such a pair of permutations exists, output "Yes"; otherwise, output "No". You can output each letter in any case (upper or lower).

In the first test case, $[1]$ and $[1]$ form a valid pair.

In the second test case and the third case, we can show that such a pair of permutations doesn't exist.

In the fourth test case, $[1,2,3,4]$ and $[1,3,2,4]$ form a valid pair.